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- logical deduction about inertial reference frames relative velocities

Hi,

consider the following in the context of classic mechanics and SR.

We know there exist special "frame of reference" according to free objects stay at rest or keep moving with constant uniform velocities. Suppose you single out a such reference frame according to the Newton law of inertia holds for a free object.

Now, from a purely logical point of view (just using logic reasoning), we cannot conclude that the rest reference frame of that free object is actually an inertial one. We need to add a further rule, namely the Galileo principle of relativity, to conclude that.

Does it make sense ?

consider the following in the context of classic mechanics and SR.

We know there exist special "frame of reference" according to free objects stay at rest or keep moving with constant uniform velocities. Suppose you single out a such reference frame according to the Newton law of inertia holds for a free object.

Now, from a purely logical point of view (just using logic reasoning), we cannot conclude that the rest reference frame of that free object is actually an inertial one. We need to add a further rule, namely the Galileo principle of relativity, to conclude that.

Does it make sense ?